Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Algebra 2 Honors Section 6.3 Notes: Square Root Functions and Inequalities Square Root Function: a function that contains the square root of a variable. *A type of radical function. Domain and Range of Square Root Functions: Domain: The expression under a radical has to be > 0. So, take the expression under the radical and set it ≥ 0 and that will be your domain. Range: Take the number from your domain inequality and substitute it into the expression. Your range will be all numbers ≥ or < that result. Example 1: Identify the domain and range of f x x 1. Example 2: Identify the domain and range of f x 2 x 1 3. Example 2: Identify the domain and range of f x 4 3x 1 5. Example 3: Graph each function State the domain and range. a) f x 3 x 4 2. b) Example 5: Graph the function f x 3 x 2 3. a) b) c) d) Square Root Inequalities: f x x 5 6. *An inequality involving square roots. *Graph using same method as other inequalities. -Solid or dashed line??? -Shade above or below??? (Test point.) *From endpoint, shade straight up/down. Example 6: Graph y x 1 2. Example 7: Graph y 2 x 4. a) b) c) d) Example 8: When an object is spinning in a circular path of radius 2 meters with velocity v, in meters per second, the centripetal acceleration a, in meters per second squared, is directed toward the center of the circle. The velocity v and acceleration a of the object are related by the function v 2.a a. Graph the function in the domain {a|a ≥ 0}. b. What would be the centripetal acceleration of an object spinning along the circular path with a velocity of 4 meters per second? Domain of Cube Root Functions: Domain: What type of numbers can/cannot be underneath a cube root? *Any # can be put under a cube root! Therefore, the domain of cube root functions is all real numbers. Range of Cube Root Functions: Range: What type of numbers will result from cube rooting a number? *Answers could be ANY number! Therefore, the range of cube root functions is all real numbers. Example 9: Graph the function f x 3 x . State the domain and range. (Parent function for cubed roots) Example 10: Graph the function and state the domain and range. a) f x 3 x 1 3. c) f ( x) 3 x 3 b) f x 2 3 x 2 1.